I finished the quests to become a full member of the guild and have become to guild master but the quest "become a full member of the thieves guild" with the finding the unusual gems has not been completed. Do I need to find all the gems in order for it to be completed?

You talked to Vex about them, right? It should give a new quest in your log.

I done with that quest it was a pain finding all the unusual gems.

There's two items under one quest -find all the gems and -become a full member. If I am leader of the guild, wouldn't I be a full member?

Yes; it sounds like a bug but follow Korr's advice, if you haven't. Talk to Vex about the gems and see if it changes your quest log.

I did that quest long time ago it wont change till he done with that quest.

Done with the gems part of the quest?
I have done business with Vex many times.

You're already a full TG member---you wouldn't have been able to access the Cistern area or any of the TG services (training, reduced prices trading with Tonila etc) otherwise. You also wouldn't have been able to receive any of the TG quests, which means you would've never been able to become TG master.

The crown gem quest is a Radiant quest and completely optional. You only need complete it if you're a collection fanatic, crave 100% completion/achievement and/or want to display it as a trophy on Mercer's desk in the Cistern. And yes, you'll need to find all of the 24 gems in order to complete this. So make sure you explore every nook and crany of every dungeon you investigate during quests/random world exploration. Same thing for houses---the gems show up in the wierdest, most exotic of places. Also most of the houses with the gems, tend to be tied into a main/side/favor quests. So you'll run into them when you enter the residence for that particular quest. Also, quite a few of these homes tend to belong to the more wealthier of Skyrim's denizens. So keep an eye out when prowling at night.

The crown is suppose to be important I think. It alllows you to activate it, once it's on the pedestal in the cistern but does nothing. And also I want my Karliah in the nightingale hall.

Well not according to the hardcopy of the manual. Which wiki did you get that info from? According to the game manual you get

Yeah, but have you tried activating it.

I also found this bug on my first character. So, with my next one, I didn't talk to Vex about the unusual gem, UNTIL I received my TG armor from Tonilia. Then my quest updated "become a full member of the TG". ONLY THEN did I talk to Vex about those jewels. Somehow, when you first talk to Vex, the quest will bug out and not acknowledge that you became a full member. -.-

If you are playing on PC, you can use the "set.stage" command. Check the wikihttp://www.uesp.net/wiki/Skyrim:No_Stone_Unturned<-----

So, does that mean it won't update after finding them all?

grrr... note it's still MERCER'S desk? yargh... lol

MY desk. ME... MOI who is singlehandedly rebuilding the guild, expanding us into cities that have forgotten us and collecting all the cool braggable items at that desk. Me... the Dovahkiin... the head of the Dark Brotherhood, the Arch Mage of the Mage's College at Winterhold and decorated Thane of 4 of the 5 main holds in Skyrim, rapidly working on the 5th... this little red haired lady who is the boss and a Nightengale and also decorated military leader in the Emperial army... argh!

just sayin... if Vex tells me one more time to get off my butt and go do something I'mma find a way to figure out what she's doing down there in the Cistern all day... besides taking baths to make Delvin crazy.

LMAO! You tell 'em Julienne!!!!!!!!!

I have the same problem. It never "completed" the quest line about becoming a full member of the Thieves' guild even though I am a member and talked to Vex to get the next stage of the quest.

lol yeah I know right?

@ Ji Soo -- I'm thinking the perk is what you get when you click on it. But again, I don't see that in the manual anywhere. So it's possible it could have been omitted/misprinted somehow. I also didn't talk to Vex before I got my TG armor from Tonila, so I'm still in process of "becomming a full TG" despite being Guildmaster. I guess I'll just have to wait until I have the complete set and then see. I'm still 15/24 on this one.

edit: Vex the mystery woman. You know about the running forum joke between Vex and Delvin? Rumor Mill says Vex actually likes Delvin, because she simply refuses to leave the Flagon! She seems obsessed with sitting around on her bum all day, and harrassing Delvin with snail mail accusing him of stalking her! Wonder if CK can rectify this intriguing romance drama in the TG? Why isn't she marriage material anyway?? I'd really love to see some DLC that included a side quest backstory on Vex.